Before any structural path can be trusted, the measurement model must prove two things: items belonging to the same construct hang together (convergent validity) and constructs that are supposed to be different really are different ([discriminant validity](/knowledge-hub/discriminant-validity)). Both are judged by numeric thresholds that examiners and reviewers check line by line. Here they are, with what to do when you miss them.
Convergent validity: the three checks
- Outer loadings ≥ 0.708 — squaring 0.708 gives 0.50, meaning the construct explains at least half of each item's variance. Loadings 0.40–0.708 are candidates for removal, but delete only if doing so lifts AVE or composite reliability above threshold — content coverage outranks cosmetic gains.
- [AVE](/knowledge-hub/average-variance-extracted) ≥ 0.50 — the construct explains, on average, more than half its items' variance. This is the convergent-validity criterion.
- [Composite reliability](/knowledge-hub/composite-reliability) 0.70–0.95 (and/or Cronbach's alpha ≥ 0.70) — internal consistency; above ~0.95 suggests redundant items. Compute alpha quickly with our calculator.
Discriminant validity: Fornell-Larcker, cross-loadings, HTMT
Fornell-Larcker criterion (the classic)
The square root of each construct's AVE must exceed that construct's correlation with every other construct. In the matrix SmartPLS prints, the diagonal (√AVE) must be the largest number in its row and column. It's still expected in most theses — but it's known to miss problems when loadings vary little.
HTMT (the current standard)
The [heterotrait-monotrait ratio](/knowledge-hub/htmt-ratio) compares between-construct correlations to within-construct correlations. Thresholds: HTMT < 0.85 for conceptually distinct constructs (the strict criterion), < 0.90 for conceptually similar ones (e.g. satisfaction and loyalty). The stronger test: bootstrap the HTMT and show its confidence interval stays below 1.0. Reviewers in better journals now treat HTMT as the primary evidence, with Fornell-Larcker as supplementary.
Cross-loadings (supporting evidence)
Each item should load higher on its own construct than on any other. Cross-loading violations usually foreshadow HTMT failures — check them during pilot analysis, not after full data collection.
When a construct fails
- 1AVE below 0.50 — remove the weakest-loading item(s) one at a time, re-estimating each time; if AVE stays low, the items don't measure one thing — revisit the construct's definition and source scale.
- 2HTMT above threshold — the two constructs overlap empirically. Options, in order of preference: check for wrongly-assigned items; merge the constructs if theory permits (respecify the model); or defend distinctness with the bootstrapped HTMT CI < 1 test.
- 3Never delete items purely to pass thresholds while gutting the construct's meaning — examiners ask 'what does the construct still measure?' and adapted-scale studies die on that question.
One measurement-model table: construct, items, loadings, alpha, CR, AVE — followed by the Fornell-Larcker matrix and the HTMT matrix. State each threshold with a citation in the table note. This single section pre-empts the most common quantitative viva and review questions. The same standards apply in CB-SEM (AMOS) with CFA-based equivalents — see model fit indices in AMOS.
Once the measurement model passes, move to the structural model and bootstrapping interpretation. If a stubborn construct keeps failing, our SmartPLS mentoring can usually locate whether the problem is items, data or theory in a single session.
Frequently asked
What is the minimum AVE value?+
0.50 — the construct must explain at least half of its items' average variance. An AVE of 0.45 with composite reliability above 0.70 is sometimes defended citing Fornell & Larcker's original argument, but expect to justify it explicitly.
Is HTMT 0.85 or 0.90 the cutoff?+
0.85 for constructs that should be clearly distinct; 0.90 is defensible for conceptually adjacent constructs. If you're between the two, run the bootstrapped HTMT confidence-interval test — an upper bound below 1.0 is the strongest available evidence.
Do I need both Fornell-Larcker and HTMT?+
In practice, yes — HTMT is the methodologically current criterion, while Fornell-Larcker remains the convention most Indian examiners expect to see. Reporting both (plus cross-loadings in an appendix) closes the question completely.
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